Brown the butter by cooking it over medium heat in a stainless-steel saucepan. Whisk so that the butter melts evenly. As it cooks, the butter will begin to foam, so be sure to whisk frequently to check underneath the bubbly surface. Soon little browned bits will form at the bottom. As soon as they begin to form, remove from heat. Transfer to a bowl and cool to room temperature (still liquid).
Preheat oven to 375°F and set aside an ungreased baking sheet.
In a medium bowl, combine all-purpose flour, baking soda, and salt. Whisk and set aside.
In a large bowl, beat browned butter, brown sugar, and granulated sugar on medium speed until light and fluffy, about 4 minutes. Add egg and vanilla and mix well.
Add dry ingredients to butter mixture and mix on low speed until just combined. Add chocolate chips and mix to combine.
Spoon the cookie dough out using a cookie scoop or about 2 tablespoons worth of dough onto the baking sheet, placed 2-inches apart. Bake until golden brown around the edges, about 10 to 12 minutes. Cool on baking sheet for 5 minutes, then transfer to wire rack and cool completely.